with \(\Sigma _F\)  a covariance defining asymptotic freqentist coverage of the pseudo-true values. [1]} give this covariance in terms of the model elements. In contrast, if \(\varphi ,\tilde{\theta },\theta \sim {\tilde{p}}^{(k)}_\delta (\varphi ,\tilde{\theta },\theta |Y,Z)\) 
are samples from the \(\delta \) -SMI posterior then
\(\sqrt{n}(\varphi -\hat{\varphi }_\delta ,\tilde{\theta }-\widehat{\tilde{\theta }}_\delta ,\theta -\hat{\theta }_\delta )\stackrel{D}{\longrightarrow } N(0,\Sigma _C),\) 
